Can I use Speaking Email with the app ‘Mailbox’? - About Speaking Email
Yes. They work great together. Because both apps use your Gmail account directly, you can use them both to help take control of your inbox.
There are a number of folders you can customise in Speaking Email and you can set these to Mailbox folders if you wish - for example set your ‘star folder’ to be "[Mailbox]/To Read" or "[Mailbox]/Later".